Work done by a force F along a vector P is F.P (dot product). So total work done is
F.P + F.A
where A=<1,-3,4>, P=<7-1, 2-(-3), 5-4>
and F=15<1,2,2>/sqrt(1^2+2^2+2^2)=<5,10,10>
The division by sqrt(...) is required to normalize the direction vector to a unit vector.